* Nadal still yet to drop a set in the tournament
* Azarenka overcomes tough challege from Cornet
* Kvitova and Kuznetsova both beaten (Updates with Nadal winning)
NEW YORK, Aug 31 (Reuters) - Rafa Nadal, growing in confidence with each match, blasted his way into the fourth round of the U.S. Open on Saturday with an ominous display.
The Spaniard turned on a masterclass of power and precision at the last grand slam of the year as he brushed aside Croatia's Ivan Dodig 6-4 6-3 6-3.
The world number two has been in great form in the past month, winning warm-up tournaments in Montreal and Cincinnati.
He has not dropped a single set in getting to the last 16 at Flushing Meadows and said he was still improving.
"I played better today than in the previous matches. (That's) always a positive thing," he said.
Nadal's next opponent is Germany's Philipp Kohlschreiber, who beat towering American John Isner 6-4 3-6 7-5 7-6 (5), with Roger Federer looming as a possible quarter-final opponent.
While Nadal cruised into the next round, a feisty Victoria Azarenka dropped her first set of the tournament before recovering to book her place in the last 16.
A finalist last year and one of the favourites to win the title this season, Azarenka overcame a shaky start to beat Alize Cornet of France 6-7(2) 6-3 6-2 after Petra Kvitova and Svetlana Kuznetsova crashed out of the women's draw on a day of upsets.
Kvitova, the 2011 Wimbledon champion and seventh seed at Flushing Meadows, fell 6-3 6-0 to American wildcard Alison Riske.
Then Kuznetsova, a former U.S. Open and French Open champion, was beaten 7-5 6-1 by Italy's Flavia Pennetta.
Russia's Maria Kirilenko, seeded 14th, was thrashed 6-0 6-1 by in-form Romanian Simona Halep, while former world number one Ana Ivanovic had to dig deep to avoid joining the growing casualty list.
The Serbian was on the brink of defeat in her centre court match against American Christina McHale before recovering to win 4-6 7-5 6-4. She plays Azarenka next.
"I know what to expect," said Ivanovic. "I really want to play against the best and challenge myself, because I'm ready to take them on."
As the world number two and reigning Australian Open champion, Azarenka is expected to go deep into the tournament but the Belarussian was given a tough workout from Cornet and allowed her frustrations to boil over when the umpire ordered a point she had won be replayed.
"That was the most ridiculous thing there is," Azarenka said.
The U.S. Open is the only grand slam where Kvitova has failed to at least make the quarter-finals and the Czech said she was unable to play near her best on Saturday after contracting a virus.
"Unfortunately I was lying in the bed yesterday and I had a fever," Kvitova said. "I tried to play, tried to fight. But my body wouldn't let me fight."
Drained of energy, Kvitova said she was unable to practise on Friday and went to a Manhattan doctor to find out what was wrong.
"I had a blood test to see if it was bacteria and virus and it was virus," she said. "I didn't have any sore throat or anything like that. I had just a very high fever."
Riske burst into tears after her win. The 23-year-old, who still travels with a security blanket that was given to her on the day she was born, has had a long road to her first fourth round appearance at a grand slam.
She first tried to qualify for the U.S. Open in 2007 and had never won a main draw match until this year. Now she is through to the last 16, and facing a showdown with Daniela Hantuchova, who saved four match points in her 3-6 7-5 7-6(4) win over Israeli qualifier Julia Glushko.
"The blankie story is out," Riske said. "I'm used to it now. I can't deny it now. It's getting smaller by the week. It can fit in the palm of my hand."
Spain's David Ferrer, the fourth seed, joined Nadal in the round of 16 when he defeated Kazakhstan qualifier Mikhail Kukushkin 6-4 6-3 4-6 6-4 victory.
Canada's Milos Raonic, seeded 10th, also made it through safely, beating Feliciano Lopez 6-7 (4) 6-4 6-3 6-4. (editing by Nick Mulvenney)